Asymptotic theory is based on the principle that the shape of the light field with depth gradually transforms from being dependent on the incident surface light field to being constant azimuthally and dependent only on the absorption and scattering properties of the water column. Properties such as the average cosine of the oceanic light field in the asymptotic regime, μ¯∞, are thus strictly inherent optical properties (IOPs). Because of the close link between asymptotic light fields and IOPs, radiative transfer approximations (RTAs) for the asymptotic regime have been adapted for use in algorithms describing surface remote sensing reflectance RRS ( = Lu/Ed) in terms of the IOPs. For such algorithms to have utility, the asymptotic average cosine needs to be parameterized in terms of IOPs useful for ocean color remote sensing. With this motivation, μ¯∞is approximated as a function of the ratio of total backscattering to total absorption, bb/a. An additional variable in assessments is the fractional water content of pure seawater in total backscattering, ηbb. A full range of representative phase functions for natural particle fields is included in the analysis using the Fournier-Forand analytical approximation. Analytical expressions for multi-order polynomial fits are provided for μ¯∞ as a function of bb/a for each ηbb assessed, for ηbb ≤ 0.49, and for the entire data set. The full range of phase function shapes were included in each fit. Percent absolute errors were a modest 3.4% for the fit for the entire data set. Additionally, a key assumption by Zaneveld that the attenuation coefficient for upwelling nadir radiance KLu in surface waters should be approximately equivalent to the attenuation coefficient in the asymptotic regime K∞ was evaluated. Results provide justification and relationships for the targeted application of asymptotic parameters in ocean color RTAs for the surface ocean.